These types of problems were highlighted by Birkhoff and von Neumann, who took them as evidence for the failure of classical logic in the context of quantum theory. The principal aim of their essay on quantum logic was to “discover what logical structures one may hope to find in physical theories which, like quantum mechanics, do not conform to classical logic” ([1]}, p. 823). The expression quantum logic in this paper must be clarified, since it refers to a quantum propositional calculus in the form of a “calculus of linear subspaces with respect to set products, linear sums, and orthogonal complements” which “resembles the usual calculus of propositions with respect to and, or, and not” (ibid.), where the logical propositions are associated to measurements, tests on quantum systems.Cf. [2]} and [3]} for a systematic introduction to various forms of quantum logic, and to [4]} for historical and philosophical discussions on the topic.
